Auxiliary Functions for STO Molecular Integrals: Si, Ci and Ei
The renewed interest in molecular integrals for Slater-type orbitals (STO’s) is increasing the urgency of the development of more efficient methods for calculating sine, cosine, and exponential integrals. The sine integral arises in expansions of the Fourier transform of a two-center STO product, and the exponential integral occurs in analytic multi-center integral formulations. The standard analytical methods for evaluating these integrals include the power series expansions for small arguments, and continued-fraction or asymptotic expansions for large arguments. None of these methods are fast for a large intermediate argument range, and the integrals are often evaluated by finite numerically fitted Chebyshev or rational-fraction expansions.
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